A time-dependent density-functional formalism is developed for many-electron systems subjected to external electric and magnetic fields with arbitrary time dependence. The single-particle current density is shown to determine uniquely the time-dependent scalar and vector potentials characterizing the system, and hence also the many-particle wave function. A Levy-type universal functional is defined, and practical schemes for the calculation of electron density and the current density through hydrodynamical as well as a set of single-particle Kohn-Sham-like equations are proposed. The gauge invariance of the present self-consistent formalism is also proved.

It is shown that, in the phase-space representation of quantum mechanics, the uncertainty relation can be stated in terms of the integral invariant of Poincaré. The uncertainty relation for spreading free wave packets is discussed as an illustrative example. This phase-space approach can be extended to the relativistic regime. It is shown that Lorentz boosts are area-preserving canonical transformations in the phase space of the light-cone variables. The harmonic oscillator is discussed in detail as an illustrative example for the covariant realization of the uncertainty principle.

High-accuracy approximations of the bound-state energies of the Hulthén potential are obtained by means of algebraic perturbation calculations which are based upon the dynamical-group structure SO(2,1).

The density dependence of dtμ molecular formation has been treated as a line-broadening process in the impact approximation. In the present paper, elastic cross sections and their coherent difference are calculated for ${\mathrm{D}}_2$+${\mathrm{D}}_2$ and (dtμ)dee+${\mathrm{D}}_2$ collisions. Together with the rotationally inelastic cross sections previously calculated [Phys. Rev. A 37, 329 (1988)] using the same accurate intermolecular potential, this provides all cross sections needed for evaluation of the width in the impact approximation. The impact width is dominated by elastic scattering and, at the temperature 23 K and liquid-hydrogen density, has the value 14 meV, which is more than three times the previously calculated value.

In the semiclassical approximation, the quantum-mechanical scalar product between two quantum states is governed by (1) the areas of overlap in phase space of these states and (2) interference between the probability amplitudes contributed by these areas. We compare and contrast this principle with Wigner’s concept of pseudoprobabilities in phase space and illustrate the essential points of both treatments by the oscillations in the photon distribution of a highly squeezed state.

The large-dimensional approach to atomic physics is extended to accommodate mass-polarization and recoil contributions. This approach, which does not rely on partitioning of the potential into subterms, but instead treats the Hamiltonian for large dimension exactly and incorporates corrections order by order in the dimension, is of interest for exotic atoms and molecules. Application of the results to the helium atom and the dimuonic-helium ground-state energy is considered.

The adiabatic hyperspherical technique is applied to a three-body system interacting via a short-range potential. Analytical expressions for the effective hyper-radial potential have been obtained without explicit use of the two-body potential. Possible loosely bound states of the system have been analyzed quantitatively and the result confirms the prediction by V. Efimov (Yad. Fiz. 10, 107 (1969) [Sov. J. Nucl. Phys. 10, 62 (1970)]). At the same time, some new characteristics of the three-body system are obtained.

We present a technique to evaluate the capture amplitude from an arbitrary initial state of the target to an arbitrary final state of the projectile within the framework of target continuum distorted-wave theory recently derived and developed by Crothers and Dunseath. Both integrals in their first-order transition amplitude, $T^{\mathrm{}\left(1\right)\mathrm{}}$, are evaluated into closed form, resulting in a finite number of terms. From our general expression of the nlm-n’l’m’ amplitude, the evaluation of $T^{\mathrm{}\left(1\right)\mathrm{}}$ for the 1s-1s capture is straightforward. With this technique, it is now convenient to calculate capture cross sections from higher angular momentum states of the target to any projectile states, which are not so easy to calculate in other second-order theories such as the strong-potential Born approximation.

Total cross sections ($Q_T$’s) have been measured for 1–500-eV positrons and electrons scattered by ${\mathrm{O}}_2$, ${\mathrm{CH}}_4$, and ${\mathrm{SF}}_6$ using a beam-transmission technique. The positron $Q_T$’s are compared with the corresponding electron $Q_T$’s for each target gas. It is found that the positron $Q_T$’s are, in general, lower than the electron results. There are no prominent structures observed for positron scattering at low energies that would be comparable to the narrow shape resonances observed for electrons scattering from various molecules, such as ${\mathrm{SF}}_6$. The positron $Q_T$ curve for ${\mathrm{CH}}_4$ reveals a significant increase in the vicinity of its positronium formation threshold, while the ${\mathrm{O}}_2$ and ${\mathrm{SF}}_6$ curves are monotonically increasing in this vicinity. At the highest energies investigated, there are indications of a tendency toward merging of the positron and electron $Q_T$’s for these gases. Interesting similarities are found in a comparison of the present positron and electron $Q_T$ curves for ${\mathrm{CH}}_4$ with prior comparison measurements for argon.

The well-known Spencer-Fano theory of electron-degradation spectra treats time-independent cases, in which the medium is subjected to stationary irradiation. We present a generalization to time-dependent cases, showing how to calculate the temporal behavior of the electron-degradation spectrum and of related quantities such as the yield of ions or excited states that are produced under nonstationary irradiation. The generalized theory indicates new aspects of electron-degradation phenomena, which are basic to radiation physics and chemistry as well as to applications such as gaseous electronics, upper-atmospheric physics, and astrophysics.

Energy pooling (EP) has been observed in Sr vapor following pulsed optical excitation to the 5${}^3$$P_1$ state. From the time-dependent radiative decay of 6${}^3$$S_1$ and of $6^1$${\mathit{S}}_0$ via the cascade resonance line, the EP rate coefficients have been investigated for the following: Sr(5 ${}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}$)+Sr(5${}^3$${\mathit{P}}_{\mathit{J}\mathcal{’}}$) &Sr${(5\mathrm{}}^1$$S_0$) +Sr(6 ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ or $6^1$$S_0$). The values of $k_{11}$ have been measured, as well as $k_{\mathrm{JJ}\mathcal{’}}$ averaged over a thermal distribution of 5 ${}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}$ populations. The time-dependent Sr($5^3$$P_J$) densities were measured by absorption of lines from a Sr lamp crossing the excitation region. The rate coefficients are surprisingly large; in spite of the small statistical weights of these product states, they are nearly gas-kinetic. The dependence of the rates upon spin, J, and energy defect ΔE has also been examined.

The stimulated Compton scattering of photons between two oppositely propagating coherent lights by a relativistic electron moving along the same line is studied analytically. The system is described in a moving frame so that the electron becomes nonrelativistic and the frequencies of the two lights coincide. Except for the replacement of the static wiggler by a propagating light, our system is essentially the same as a free-electron laser working in the Compton regime and described in the usual Bambini-Renieri frame. The Q representation of two-mode coherent states is adopted to describe the radiation fields, and the electron states are expressed in terms of plane waves. A perturbative solution, with the quantum recoil of the electron as the perturbation parameter, of the time evolution of the system is carried out far beyond the first order. It demonstrates that two nonclassical effects, i.e., squeezing and photon antibunching, occur as results of the scattering. It also confirms once more the fact that quantum recoils play the exclusive role in generating such nonclassical photon states. A very important improvement in the present treatment is that the electron part of the density matrix is traced out before the calculation of the squeezing effect. As a result, it is found that there is no squeezing if the initial state is a vacuum. This is, perhaps, a significant new discovery. Many-electron effects are ignored in the present study.

Absolute differential cross sections for the 3${\mathit{p}}^6$${\mathrm{}}^1$${\mathit{S}}_0$ →3${\mathrm{p}}^5$${(}^2$${\mathrm{P}}_{1/2}$)4s, ${(}^2$$P_{3/2}$)4s excitation in argon have been measured at impact energies of 400 and 500 eV, and at scattering angles between 1.75° and 10.3° by electron-energy-loss spectroscopy. The integrated cross sections and generalized oscillator strengths (GOS’s) have also been determined at 400 and 500 eV. The optical oscillator strengths have been determined, by extrapolating the GOS’s to zero momentum transfer, as ${0.222}_{\mathrm{-}0.03}^{+0.02\mathrm{}}$ for the ${(}^2$${\mathrm{P}}_{1/2}$)4s state and ${0.058}_{\mathrm{-}0.008}^{+0.005\mathrm{}}$ for the ${(}^2$${\mathrm{P}}_{3/2}$)4s state. These data are compared with the results of other optical measurements in the vacuum-ultraviolet region. The errors are estimated to be less than 14%.

We introduce a new nonsingular scattering integral equation, which is suitable for the investigation of the total (also off-shell) transition matrix in arbitrary dimension n≥2. In particular, the low-energy properties are derived and lead, in connection with spin-polarized atomic hydrogen H↓, to the low-temperature behavior of two- and three-body surface processes. In addition, for three dimensions the method leads in a natural way to a separable approximation to the T matrix for all energies, with the possibility of formulating a procedure for optimizing this approximation. To show the practicability of the equation we also present numerical results for both n=2 and n=3.

We present the result of a theoretical estimation of the photoionization cross sections for transitions from the excited 3snd ${}_{}{}^1{}_{}{}^{}D$ states of Mg to the doubly excited 3pnl ${}_{}{}^1{}_{}{}^{}F$ autoionization states above the first ionization threshold. In particular, we examine in detail the effect of the multielectron interactions both in the initial and the final states of the transition. The calculated excitation energy and the width for the 3pnl${}^1$F autoionization series are reported. The experimental implications are also discussed.

Using Doppler-free two-photon absorption spectroscopy, we have measured hyperfine splitting constants as well as isotopic level shifts of the 6$s^2$np ${}_{}{}^2{}_{}{}^{}P_{1/2}^{}{}_{}{}^{}$,3/2 states (n=7–10) in ${}_{}{}^{203}{}_{}{}^{}\mathrm{Tl}$ and ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$. Calculations for hyperfine constants and electron density at the nucleus have been performed by the Dirac-Fock method. The experimental results are compared with these calculations as well as with the predictions of the semiempirical theory.

Two-photon excitation from the ${}_{}{}^1{}_{}{}^{}\mathrm{D}_2^{}{}_{}{}^{}$ level of atomic sulfur was used to probe the previously unobserved, even-parity singlet levels in the region between the two lowest ionization thresholds. Several new Rydberg series were observed and assigned to the ${(}^2$D°)np and ${(}^2$D°)nf configurations. Although these levels are energetically allowed to autoionize into the ${}_{}{}^4{}_{}{}^{}\mathrm{e}_{}^{\mathrm{-}}{}_{}{}^{}$ continuum, autoionization is forbidden within LS coupling, resulting in very narrow linewidths.

Completely numerical multiconfiguration Hartree-Fock (MCHF) methods are used to calculate the photoionization cross section of atomic sodium in its ground state for incident photon energies in the single-channel region between the first (3$s^{\mathrm{-}1}$${)}^1$S and second (2$p^{\mathrm{-}1}$${)}^3$P ionization thresholds. Particular attention is focused on obtaining accurate cross-sectional values in the threshold and Cooper-minimum region up to ∼5 eV kinetic energy, where there is the possibility of a sensitivity of results to the quality of the ground-state wave function and final-state potential, and on incorporating the effects of dynamical core polarization in the final state, which are particularly important in the ∼5–15-eV kinetic energy region. These attributes are incorporated in the MCHF procedure by including appropriate doubly excited configurations in the ground state and $L^2$ polarization pseudostates in the final-state wave function. Provision is made in the final-state calculation for the simultaneous variational determination of the continuum function, of the orbitals comprising a basis for the $L^2$ polarization pseudostates, and of the configuration-mixing coefficients at each photon energy. The cross sections calculated in this way using length and velocity forms are in good agreement over the entire incident photon energy range considered, suggesting that converged values may be obtained in this interval from the present development. The very small effects of spin-orbit interaction on the photoionization cross section are neglected in the present calculations, in accordance with previously reported observations. Comparisons are made with available experimental values and with other computational studies in various approximations, and comments are provided on the origins of discrepancies between the present and previously reported measured and calculated values.

We calculate, using the Dirac-Slater potential, the anomalous x-ray atomic scattering factor f’ for the elements F, Na, Si, Cl, K, and Ca and compare the calculated values with Creagh’s experimental values [D. Creagh, Phys. Lett. 103A, 52 (1984). For certain cases the theoretical values agree with the experimental values, but for most cases the theory disagrees with the experiment, even when experimental errors are taken into account. The experimental values tend to be lower than the theoretical values, in contrast to the cases of Si for Ag Kα¯ and Mo Kα¯ energies.

Extensive ab initio calculations at coupled-electron-pair approximation and multireference configuration interaction levels have been performed for the two lowest states X ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ and $A^2$Π of ${\mathrm{HeNe}}^{+}$. Spin-orbit coupling has been included on a semiempirical basis in order to account for the strong mixing between the X ${}_{}{}^2{}_{}{}^{}\Sigma _{1/2}^{+}{}_{}{}^{}$ and $A_2^2$${\Pi }_{1/2}$ components, which influences the properties of both these states in the experimentally observed region at large internuclear distances.

After a careful analysis of electron-correlation effects in the X state, we were able to interpret the observed spectrum of ${\mathrm{HeNe}}^{+}$ and to explain the large discrepancies between experiment and previous ab initio calculations. We conclude that the determination of the equilibrium properties such as $R_e$, ${\omega }_e$, etc. from the observed vibrational intervals and rotational constants of high vibrational levels has led to incorrect ‘‘experimental’’ values for the $X^2$${\Sigma }_{1/2}^{+}$ ground state. Our predictions for ${}_{}{}^4{}_{}{}^{}\mathrm{HeNe}_{}^{+}{}_{}{}^{}$ are [in ${\mathrm{cm}}^{\mathrm{-}1}$, experimental results from Dabrowski and Herzberg, J. Mol. Spectrosc. 73, 183 (1978) in parentheses] (i) X ${}_{}{}^2{}_{}{}^{}\Sigma _{1/2}^{+}{}_{}{}^{}$ state: $R_e$=1.43 (1.300) Å, $D_e$=5492 (6216±300), ${\omega }_e$=913 (1308); the vibrational intervals ΔG(v+half) are 349 (341.59), 229 (233.42), 135 (146.27), and the corresponding rotational constants $B_v$ are 1.610 (1.58983), 1.361 (1.35755), 1.083 (1.09037), 0.814 (0.8431) for v=6,7,8,9, respectively; (ii) $A_2^2$${\Pi }_{1/2}$ state: $R_e$=2.36 (2.318) Å, $D_e$=328 (347.2), ΔG(half)=119 (129.69), $B_0$=0.840 (0.86571), $B_1$=0.674 (0.71658). Two more vibrational levels should exist for this state, as is also suggested recently by another experiment and by semiempirical model calculations.

Results of similar quality were obtained also for ${}_{}{}^3{}_{}{}^{}\mathrm{HeNe}_{}^{+}{}_{}{}^{}$. The calculated properties of the experimentally unobserved $A_1^2$${\Pi }_{3/2}$ state differ very much from those of the $A_2$ ${}_{}{}^2{}_{}{}^{}\Pi _{1/2}^{}{}_{}{}^{}$ component of the same $A^2$Π state.